Fox, M.D., Frizzell, L.A., FrankS, L. A, Darken, L.S., James, R B. "Medical Imaging The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Fox, M..D., Frizzell, L.A., Franks, L.A., Darken, L.S., James, R.B. “Medical Imaging” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
116 Medical lmaging University of Connecticut Leon a. frizzell 116.1 Tomography Larry A Franks Tomography. Single Photon Emission Computed Tomography. Magnetic Resonance Imaging. Imaging Sandia national laboratories 116.2 Ultrasound Larry S Darken Fundamentals of Acoustics. Principles of Pulse-Echo Ultrasound. Future Developments 116.3 Semiconductor Detectors for Radiation measurements Ralph B. James Cryogenic Detectors. True Room-Temperature Detectors sandia national laboratories Silicon Detectors. Prices and Availability 116.1 Tomography M.D. Fox The term tomography derives from the Greek tomos(cutting)and grapho( to write). Originally the term was applied to sectional radiography achieved by a synchronous motion of the x-ray source and detector in order to blur undesired data while creating a sharp image of the selected plane. The term tomography was used to distinguish between such slices and the more conventional plain film radiograph, which represents a two- dimensional shadowgraphic superposition of all x-ray absorbing structures within a volumetric body. Computerized tomography, also known as computerized axial tomography, was introduced by EMI, Ltd. n 1973 and transformed medical imaging by obviating the superposition of intervening structures present conventional radiographic imag in ges. Initially, the clinical application was for imaging the head, but soon the technique found wide application in body imaging As medical imaging has evolved into a multimodality field, the meaning of tomography has broadened to include any images of thin cross-sectional slices, regardless of the modality utilized to produce them. Thus, omographic images can be generated by magnetic resonance imaging(MRI), ultrasound (US), computerized tomography(CT), or such nuclear medicine techniques as positron emission tomography(PET) or single photon emission computerized tomography(SPECT). For the purposes of this discussion we will cover all of the foregoing modalities with the exception of ultrasound, which will be treated separately. Since the power of such computerized techniques was recognized, the practice of radiology has been revo- lutionized by making possible much more precise diagnosis of a wide range of conditions. In this necessarily brief discussion we will describe the basic physical principles of the major tomographic modalities as well as their key clinical applications. Computerized Tomography The basic concept of computerized tomography can be described by consideration of Fig. 116.1. An x-ray source is passed through an aperture to produce a fan-shaped beam that passes through the body of interest absorption along approximately parallel lines. The natural logarithm of the detected intensity will be the intesa of the linear attenuation coefficient of the object along the ray directed from the source to the detector elem If the source and the detector array are synchronously rotated about a point within the object, a number c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 116 Medical Imaging 116.1 Tomography Computerized Tomography • Positron Emission Tomography • Single Photon Emission Computed Tomography • Magnetic Resonance Imaging • Imaging 116.2 Ultrasound Fundamentals of Acoustics • Principles of Pulse-Echo Ultrasound • Future Developments 116.3 Semiconductor Detectors for Radiation Measurements Cryogenic Detectors • True Room-Temperature Detectors • Silicon Detectors • Prices and Availability 116.1 Tomography M. D. Fox The term tomography derives from the Greek tomos (cutting) and grapho (to write). Originally the term was applied to sectional radiography achieved by a synchronous motion of the x-ray source and detector in order to blur undesired data while creating a sharp image of the selected plane. The term tomography was used to distinguish between such slices and the more conventional plain film radiograph, which represents a twodimensional shadowgraphic superposition of all x-ray absorbing structures within a volumetric body. Computerized tomography, also known as computerized axial tomography, was introduced by EMI, Ltd. in 1973 and transformed medical imaging by obviating the superposition of intervening structures present in conventional radiographic images. Initially, the clinical application was for imaging the head, but soon the technique found wide application in body imaging. As medical imaging has evolved into a multimodality field, the meaning of tomography has broadened to include any images of thin cross-sectional slices, regardless of the modality utilized to produce them. Thus, tomographic images can be generated by magnetic resonance imaging (MRI), ultrasound (US), computerized tomography (CT), or such nuclear medicine techniques as positron emission tomography (PET) or single photon emission computerized tomography (SPECT). For the purposes of this discussion we will cover all of the foregoing modalities with the exception of ultrasound, which will be treated separately. Since the power of such computerized techniques was recognized, the practice of radiology has been revolutionized by making possible much more precise diagnosis of a wide range of conditions. In this necessarily brief discussion we will describe the basic physical principles of the major tomographic modalities as well as their key clinical applications. Computerized Tomography The basic concept of computerized tomography can be described by consideration of Fig. 116.1.An x-ray source is passed through an aperture to produce a fan-shaped beam that passes through the body of interest with absorption along approximately parallel lines. The natural logarithm of the detected intensity will be the integral of the linear attenuation coefficient of the object along the ray directed from the source to the detector element. If the source and the detector array are synchronously rotated about a point within the object, a number of M. D. Fox University of Connecticut Leon A. Frizzell University of Illinois Larry A. Franks Sandia National Laboratories Larry S. Darken Oxford Instruments Ralph B. James Sandia National Laboratories
APPARATUS AND METHOD FOR DETECTING CANCER IN TISSUE Raymond V. damadian Patented February 5, 1974 #3,789,832 xcerpts from Raymond Damadian's patent application It has now been found that, by measuring the degree of organization of these selected molecules in cells being studied and comparing this with the degree of organization in a known cancerous cell, cancer cells can be detected. Furthermore, it has now been found that the less the organization the greater the malignancy therefore a scale can be made to provide a standard for basing a decision on the degree of malignancy Further apparatus is provided for scanning throughout the entire body during which time the relaxation times are measured for selected nuclei and compared with standards. In this way a determination can be made of the existence of cancer together with the location and degree of malignancy of the cancerous cells This patent describes a device that uses very powerful magnetic fields to resonate the nuclei in cells in a body. Collapsing the field and measuring the relaxation times gave a comparison to healthy cells Later advances in digital signal processing have resulted in magnetic resonance imaging(MRi)equipment with color-coded image viewing of living tissue and its chemical composition. Copyright o 1995, Dew Ray Products, Inc. Used with permission. lines of data can be collected, each representing the projected density of the object as a function of lateral position and angle number of mathematical techniques can and have been used to recover the two-dimensional distribution of the linear attenuation coefficient from this array of measurements. These include iterative solution of a set of simultaneous linear equations, Fourier transform approaches, and techniques utilizing back-projection followed by deconvolution[Macovski, 1983]. Conceptually, the Fourier transform approach is perhaps the most straightforward, so we will describe it in some detail e 2000 by CRC Press LLC
© 2000 by CRC Press LLC APPARATUS AND METHOD FOR DETECTING CANCER IN TISSUE Raymond V. Damadian Patented February 5, 1974 #3,789,832 Excerpts from Raymond Damadian’s patent application: ...It has now been found that, by measuring the degree of organization of these selected molecules in cells being studied and comparing this with the degree of organization in a known cancerous cell, cancer cells can be detected. Furthermore, it has now been found that the less the organization the greater the malignancy, therefore a scale can be made to provide a standard for basing a decision on the degree of malignancy... ...Further apparatus is provided for scanning throughout the entire body during which time the relaxation times are measured for selected nuclei and compared with standards. In this way a determination can be made of the existence of cancer together with the location and degree of malignancy of the cancerous cells present.... This patent describes a device that uses very powerful magnetic fields to resonate the nuclei in cells in a body. Collapsing the field and measuring the relaxation times gave a comparison to healthy cells. Later advances in digital signal processing have resulted in magnetic resonance imaging (MRI) equipment with color-coded image viewing of living tissue and its chemical composition. (Copyright © 1995, DewRay Products, Inc. Used with permission.) lines of data can be collected, each representing the projected density of the object as a function of lateral position and angle. A number of mathematical techniques can and have been used to recover the two-dimensional distribution of the linear attenuation coefficient from this array of measurements. These include iterative solution of a set of simultaneous linear equations, Fourier transform approaches, and techniques utilizing back-projection followed by deconvolution [Macovski, 1983]. Conceptually, the Fourier transform approach is perhaps the most straightforward, so we will describe it in some detail
A Computerized Tomography(CT) Detector Array Detector Array Source B. Positron Emission Tomography(PET collimator C. Single Photon Emission Computed Tomography FIGURE 116. 1 Comparison of three photon-based tomographic imaging modalities. Fig. 116.1(A)and assuming parallel rays, the intensity picked up by the detector array can be expresse L,()=Io exp[-a(x,y)dx] where a(x,y) represents the linear attenuation coefficient to x-ray photons within the body as a function of x,y position, and Io is the source intensity. Rearranging, we see that a, (y)=a(x, y)dx=In(L (y)/Iol where a(y)is the projected attenuation function Taking a one-dimensional Fourier transform of this projected density function we see that Fa(y)=A(f)=∫∫以xy减e形yb where A, (fy) is the Fourier transform of a single line of detected data. But this can also be written c2000 by CRC Press LLC
© 2000 by CRC Press LLC Using the coordinate system of Fig. 116.1(A) and assuming parallel rays, the intensity picked up by the detector array can be expressed as Id(y) = I0 exp[–Úa(x,y)dx] where a(x,y) represents the linear attenuation coefficient to x-ray photons within the body as a function of x,y position, and I0 is the source intensity. Rearranging, we see that where ap(y) is the projected attenuation function. Taking a one-dimensional Fourier transform of this projected density function we see that where Ap(fy) is the Fourier transform of a single line of detected data. But this can also be written FIGURE 116.1 Comparison of three photon-based tomographic imaging modalities. a y a x y dx I y I p d ( ) ( , ) ln[ ( )/ ] – = = • • Ú 0 F a y A f a x y dx e dy p py j fyy [ ( )] ( ) ( , ) – –– = = • • • • ÚÚ 2p
A,0,)=J∫以x,y减c0b Thus, the one-dimensional Fourier transform of the projection of the linear attenuation function, ap(y), is equal to the two-dimensional Fourier transform of the original attenuation function evaluated along a line in the frequency domain(in this case the f=0 line) It can readily be demonstrated that if we rotate a function a(x,y) through an angle o in the x,y plane, its transform will be similarly rotated through an angle o [Castleman, 1979]. Thus as we rotate the source and detector around the object, each projected density function detected a(p, o can be Fourier transformed to provide one radial line of the two-dimensional Fourier transform of the desired reconstructed image, A(p, oi), where p is a radial spatial frequency. The set of all A(p, o )for small angular displacements o; form a set of spokes in the transform domain which can be interpolated to estimate A(y), the two-dimensional Fourier transform of the image in rectangular coordinates. The image can then be recovered by inverse transformation of A(ffr), which can readily be carried out digitally using fast Fourier transform algorithms, i. e, a(x,y)=F [A(ofr)I While the Fourier transform approach is mathematically straightforward, many commercial scanners utilize the equivalent but more easily implemented back-projection/deconvolution approach, where each ray is traced back along its propagation axis. When all rays have been back-projected and the result summed, one obtains an approximate(blurred)image of that plane. This image can then be sharpened(deblurred)through the use deblurring function. Refer to Macovski [1983]for the details of this procsse an appropriate two-dimensional of an appropriate filter, which is usually implemented by convolving with Clinically, the impact of computerized tomography was dramatic due to the vastly increased density resolu tion, coupled with the elimination of the superposition of overlying structures, allowing enhanced differenti- ation of tissues with similar x-ray transmittance, such as blood, muscle, and organ parenchyma. CT scans of the head are useful for evaluation of head injury and detection of tumor, stroke, or infection. In the body, CT is also excellent in detecting and characterizing focal lesions, such as tumors and abscesses, and for the evaluation of the skeletal system. [Axel et al., 1983]. In recent years the advent of magnetic resonance systems has provided even greater soft tissue contrast, and thus the role of Ct has been constrained by this at times competing modality Positron Emission Tomography Unlike computerized tomography, which relies on photons produced by an external source, in the modalities of positron emission tomography(PET) and single photon emission computed tomography(SPECT), the source of radiation is a radioisotope that is distributed within the body, and thus these modalities are sometimes referred to as forms of emission computed tomography(ECT). While conventional CT can produce images based upon anatomy of organs, emission Ct techniques can quantitate the distribution of tracer materials that can potentially elucidate physiologic function. The positron or positive electron is a positively charged particle that can be emitted from the nucleus of a radionuclide. The positron travels at most a few millimeters before being annihilated by interaction with a egative electron from the surrounding tissue. The product of this event is the emission of 511-keV gamma ray photons which travel in almost exactly opposite directions. The detectors themselves can be either discrete detectors or a modified Anger camera like those used in conventional nuclear imaging. A coincidence detector is employed to limit recorded outputs to cases in which events are detected simultaneously in both detector arrays, thus reducing the pickup of noise or scattering A possible detection scheme is illustrated in Fig. 116. 1(B). The detector arrays shown can be made energy selective to eliminate lower energy scattered gamma rays. While the distribution of radioactivity can be recon- structed using the reconstruction from projection techniques described in the section on CT Hurculak, 1987 e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Thus, the one-dimensional Fourier transform of the projection of the linear attenuation function, ap(y), is equal to the two-dimensional Fourier transform of the original attenuation function evaluated along a line in the frequency domain (in this case the fx = 0 line). It can readily be demonstrated that if we rotate a function a(x,y) through an angle f in the x,y plane, its transform will be similarly rotated through an angle f [Castleman, 1979]. Thus as we rotate the source and detector around the object, each projected density function detected ap(r,fi ) can be Fourier transformed to provide one radial line of the two-dimensional Fourier transform of the desired reconstructed image, A(r,fi ), where r is a radial spatial frequency. The set of all A(r,fi ) for small angular displacements fi form a set of spokes in the transform domain which can be interpolated to estimate A(fx,fy), the two-dimensional Fourier transform of the image in rectangular coordinates. The image can then be recovered by inverse transformation of A(fx,fy), which can readily be carried out digitally using fast Fourier transform algorithms, i.e, a(x,y) = F–1[A(fx,fy)] While the Fourier transform approach is mathematically straightforward, many commercial scanners utilize the equivalent but more easily implemented back-projection/deconvolution approach, where each ray is traced back along its propagation axis. When all rays have been back-projected and the result summed, one obtains an approximate (blurred) image of that plane. This image can then be sharpened (deblurred) through the use of an appropriate filter, which is usually implemented by convolving with an appropriate two-dimensional deblurring function. Refer to Macovski [1983] for the details of this process. Clinically, the impact of computerized tomography was dramatic due to the vastly increased density resolution, coupled with the elimination of the superposition of overlying structures, allowing enhanced differentiation of tissues with similar x-ray transmittance, such as blood, muscle, and organ parenchyma. CT scans of the head are useful for evaluation of head injury and detection of tumor, stroke, or infection. In the body, CT is also excellent in detecting and characterizing focal lesions, such as tumors and abscesses, and for the evaluation of the skeletal system. [Axel et al., 1983]. In recent years the advent of magnetic resonance systems has provided even greater soft tissue contrast, and thus the role of CT has been constrained by this at times competing modality. Positron Emission Tomography Unlike computerized tomography, which relies on photons produced by an external source, in the modalities of positron emission tomography (PET) and single photon emission computed tomography (SPECT), the source of radiation is a radioisotope that is distributed within the body, and thus these modalities are sometimes referred to as forms of emission computed tomography (ECT). While conventional CT can produce images based upon anatomy of organs, emission CT techniques can quantitate the distribution of tracer materials that can potentially elucidate physiologic function. The positron or positive electron is a positively charged particle that can be emitted from the nucleus of a radionuclide. The positron travels at most a few millimeters before being annihilated by interaction with a negative electron from the surrounding tissue. The product of this event is the emission of 511-keV gamma ray photons which travel in almost exactly opposite directions. The detectors themselves can be either discrete detectors or a modified Anger camera like those used in conventional nuclear imaging. A coincidence detector is employed to limit recorded outputs to cases in which events are detected simultaneously in both detector arrays, thus reducing the pickup of noise or scattering. A possible detection scheme is illustrated in Fig. 116.1(B). The detector arrays shown can be made energy selective to eliminate lower energy scattered gamma rays. While the distribution of radioactivity can be reconstructed using the reconstruction from projection techniques described in the section on CT [Hurculak, 1987], A f a x y dx e dy p y j x fyy (, ) (, ) –( ) –– 0 2 0 = + • • • • ÚÚ p
ne x,y source position of an event can be determined directly from the detection geometry as follows[Macovsk =xL dR/(dR+d)+xr d/(d+ dd) y=y dy/(dR+d ) yr,/(d +dD Typically a single plane is studied, and no collimators are required. a drawback of PET has been that because of the short half-lives of positron-producing radioisotopes, the use of this modality has required the presenc of an expensive cyclotron facility located near the hospital. One important radionuclide commonly used in PET is oxygen 15 with a half-life of 2.07 minutes, which can be bonded to water for measurement of cerebral blood flow or to O,/CO, to assess cerebral oxygen utilization. Another is carbon 11 with a half-life of 20.4 minutes, which can be bonded to glucose to trace glucose utilization F-18 fluorodeoxyglucose(FDG)has been used to demonstrate the degree of malignancy of primary brain tumors, to distinguish necrosis from tumor, and to predict outcome[Coleman, 1991]. Perhaps the most unusual feature of this modality is the ability to quantitate the regional metabolism of the human heart [Schelbert, 1990] Single Photon Emission Computed Tomography In contrast to PET, SPECT can be utilized with any radioisotope that emits gamma rays, including such common radioisotopes as Tc-99m, I-125, and I-131 which have been utilized in conventional nuclear imaging for the last 30-35 years and which due to their relatively long half-lives are available at reasonable cost at nearly every modern hospital. Due to the need for direction sensitivity of the detector, a collimator must be used to eliminate mma rays from other than the prescribed direction, thus resulting in a 1-2 order of magnitude decrease in quantum efficiency as compared with PET scanning [Knoll, 1983 The basic concept of SPECT is illustrated in Fig. 116.1(C). A gamma ray photon from a radionuclide with Gergy above 100 kev will typically escape from the body without further interaction, and thus the body can be regarded as a transparent object with luminosity proportional to the concentration of the radionuclide at each point. The reconstruction mathematics are similar to those derived for absorption CT, with the exception that the variable reconstructed is a source distribution rather than an attenuation coefficient some errors can be introduced in the reconstruction because of the inevitable interaction of gamma rays with overlying tissue, even at energies above 100 kev, although this can be compensated for to some extent. Detection of scattered radiation can be reduced through the use of an energy acceptance window in the detector. Technetium 99m can be used to tag red blood cells for blood pool measurements, human serum albumin for blood pool and protein distribution, or monoclonal antibodies for potential detection of individual tumors or blood cells. Emission computed tomography techniques such as PET and SPECT follow the recent trend toward imaging techniques that image physiologic processes as opposed to anatomi ic imaging of organ systems. The relatively low cost of SPECT systems has led to a recent resurgence of interest in this modality. Magnetic Resonance Imagi The basic magnetic resonance concept has been used as a tool in chemistry and physics since its discovery by Bloch in 1946, but its use expanded tremendously in the 1980s with the development of means to represent magnetic resonance signals in the form of tomographic images. Magnetic resonance imaging is based on the magnetic prop- erties of atomic nuclei with odd numbers of protons or neutrons, which exhibit magnetic properties because of their spin. The predom ant source of magnetic resonance signals in the human body is hydrogen nuclei or protons In the presence of an external magnetic field, these hydrogen nuclei align along the axis of the field and can FIGURE1162 Geometry of precessing precess or wobble around that field direction at a definite frequen proton in a static magnetic field oriented known as the Larmour frequency. This can be expressed in the z direction c2000 by CRC Press LLC
© 2000 by CRC Press LLC the x,y source position of an event can be determined directly from the detection geometry as follows [Macovski, 1983]: x ª xL dR/(dR + dL) + xR dL/(dR + dL) y ª yL dR/(dR + dL) + yR dL/(dR + dL) Typically a single plane is studied, and no collimators are required. A drawback of PET has been that because of the short half-lives of positron-producing radioisotopes, the use of this modality has required the presence of an expensive cyclotron facility located near the hospital. One important radionuclide commonly used in PET is oxygen 15 with a half-life of 2.07 minutes, which can be bonded to water for measurement of cerebral blood flow or to O2/CO2 to assess cerebral oxygen utilization. Another is carbon 11 with a half-life of 20.4 minutes, which can be bonded to glucose to trace glucose utilization. F-18 fluorodeoxyglucose (FDG) has been used to demonstrate the degree of malignancy of primary brain tumors, to distinguish necrosis from tumor, and to predict outcome [Coleman, 1991]. Perhaps the most unusual feature of this modality is the ability to quantitate the regional metabolism of the human heart [Schelbert, 1990]. Single Photon Emission Computed Tomography In contrast to PET, SPECT can be utilized with any radioisotope that emits gamma rays, including such common radioisotopes as Tc-99m, I-125, and I-131 which have been utilized in conventional nuclear imaging for the last 30–35 years and which due to their relatively long half-lives are available at reasonable cost at nearly every modern hospital. Due to the need for direction sensitivity of the detector, a collimator must be used to eliminate gamma rays from other than the prescribed direction, thus resulting in a 1–2 order of magnitude decrease in quantum efficiency as compared with PET scanning [Knoll, 1983]. The basic concept of SPECT is illustrated in Fig. 116.1(C). A gamma ray photon from a radionuclide with energy above 100 keV will typically escape from the body without further interaction, and thus the body can be regarded as a transparent object with luminosity proportional to the concentration of the radionuclide at each point. The reconstruction mathematics are similar to those derived for absorption CT, with the exception that the variable reconstructed is a source distribution rather than an attenuation coefficient. Some errors can be introduced in the reconstruction because of the inevitable interaction of gamma rays with overlying tissue, even at energies above 100 keV, although this can be compensated for to some extent. Detection of scattered radiation can be reduced through the use of an energy acceptance window in the detector. Technetium 99m can be used to tag red blood cells for blood pool measurements, human serum albumin for blood pool and protein distribution, or monoclonal antibodies for potential detection of individual tumors or blood cells. Emission computed tomography techniques such as PET and SPECT follow the recent trend toward imaging techniques that image physiologic processes as opposed to anatomic imaging of organ systems. The relatively low cost of SPECT systems has led to a recent resurgence of interest in this modality. Magnetic Resonance Imaging The basic magnetic resonance concept has been used as a tool in chemistry and physics since its discovery by Bloch in 1946, but its use expanded tremendously in the 1980s with the development of means to represent magnetic resonance signals in the form of tomographic images. Magnetic resonance imaging is based on the magnetic properties of atomic nuclei with odd numbers of protons or neutrons, which exhibit magnetic properties because of their spin. The predominant source of magnetic resonance signals in the human body is hydrogen nuclei or protons. In the presence of an external magnetic field, these hydrogen nuclei align along the axis of the field and can precess or wobble around that field direction at a definite frequency known as the Larmour frequency. This can be expressed: FIGURE 116.2 Geometry of precessing proton in a static magnetic field oriented in the z direction
Ho+△Ho Pulse Data collection window Transmit/Receive Coil IGURE 116.3 Concept of magnetic resonance imaging. The static magnetic field Ho has a gradient such that excitation at frequency fo excites only the plane P Gradient G, in the y direction is applied for time tyi causing a phase shift along the ydirection Gradient G in the x direction is applied for time t, causing a frequency shift along the x direction. Repetition of this process for different yi allows the receive coil to pick up a signal which is the two-dimensional Fourier transform of the magnetic resonance effect within the slice. f o=YH where fo is the Larmour frequency, y is the gyromagnetic ratio which is a property of the atomic element, and the magnitude of the external magnetic field. For example, given a gyromagnetic ratio of 42. 7 MHz/tesla for hydrogen and a field strength of I tesla(10 kilogauss), the Larmour frequency would be 42.7 MHz, which falls into the radio frequency range The magnetic resonance effect occurs when nuclei in a static magnetic field H are excited by a rotating magnetic field H, in the x,y plane, resulting in a total vector field M given by M=HZ+ H,(x coS Oo t+y sin @, t) pon cessation of excitation, the magnetic field decays back to its original alignment with the static field H, emitting electromagnetic radiation at the Larmour frequency, which can be detected by the same coil that Imaging As shown in Fig. 116.3, one method for imaging utilizes a transmit/receive coil to emit a magnetic field at uency fo which is the Larmour frequency of plane P. Subsequently, magnetic gradients are applied in the y and x directions. The detected signal during the data collection window can be expressed as ∫J4xy)ep-Gx+x,由 where s(x,y)represents the magnetic resonance signal at position(x,y)(GnG)are the x and y gradients, t is time within the data collection window, ty is the y direction gradient application times, and y is the gyromagnetic ratio. The two-dimensional spatial integration is obtained by appropriate geometry of the detection coil. Collecting a number of such signals for a range of tr, we can obtain the two-dimensional function S(t, t) Comparing this to the two-dimensional Fourier transform relation F(u,v)=f(x, y)exp[-i2n(ux vy )]dx dy e 2000 by CRC Press LLC
© 2000 by CRC Press LLC f0 = gH where f0 is the Larmour frequency, g is the gyromagnetic ratio which is a property of the atomic element, and H is the magnitude of the external magnetic field. For example, given a gyromagnetic ratio of 42.7 MHz/tesla for hydrogen and a field strength of 1 tesla (10 kilogauss), the Larmour frequency would be 42.7 MHz, which falls into the radio frequency range. The magnetic resonance effect occurs when nuclei in a static magnetic field H are excited by a rotating magnetic field H1 in the x,y plane, resulting in a total vector field M given by M = H z + H1(x cos w0 t + y sin w0t) Upon cessation of excitation, the magnetic field decays back to its original alignment with the static field H, emitting electromagnetic radiation at the Larmour frequency, which can be detected by the same coil that produced the excitation [Macovski, 1983]. Imaging As shown in Fig. 116.3, one method for imaging utilizes a transmit/receive coil to emit a magnetic field at frequency f0 which is the Larmour frequency of plane P. Subsequently, magnetic gradients are applied in the y and x directions. The detected signal during the data collection window can be expressed as where s(x,y) represents the magnetic resonance signal at position (x,y) (Gx,Gy) are the x and y gradients, tx is time within the data collection window, tyi is the y direction gradient application times, and g is the gyromagnetic ratio. The two-dimensional spatial integration is obtained by appropriate geometry of the detection coil. Collecting a number of such signals for a range of tyi, we can obtain the two-dimensional function S(tx,ty). Comparing this to the two-dimensional Fourier transform relation FIGURE 116.3 Concept of magnetic resonance imaging. The static magnetic field H0 has a gradient such that excitation at frequency f0 excites only the plane P. Gradient Gy in the y direction is applied for time tyi, causing a phase shift along the y direction. Gradient Gx in the x direction is applied for time tx, causing a frequency shift along the x direction. Repetition of this process for different tyi allows the receive coil to pick up a signal which is the two-dimensional Fourier transform of the magnetic resonance effect within the slice. S t t s x y i G xt G yt dx dy x yi x x y yi ( , ) ( , ) exp[– ( )] – – = + • • • • Ú Ú g Fuv ( , ) f(x, y) exp[–i (ux vy )]dx dy – – = + • • • • Ú Ú 2p
we see that the detected signal S(tty )is the two-dimensional Fourier transform of the tic resonance signal s(,y) with u=yG, t/2T,v=YG ty /2T. The gnetic resonance signal s(x,y)depends on the precise sequence of pulses of magnetic energy used to perturb the nuclei. For a typical sequence known as spin-echo consisting of a 90-degree pulse followed by a 180-degree pulse spaced at time t with the data collection at t 2t, and t, being the repetition time between 90-degree pulses, the detected magnetic resonance signal can be s(x,y)=p(1-e/T(ete/T2) where p is the proton density, and T,(the spin-lattice decay time)and T,(the spin-spin decay time)are constants of the material related to the bonding of water in cells [wolf and Popp, 1984. Typically T, ranges from 0. 2 to 1.2 seconds, while T2 ranges from 0.05 to 0.15 seconds By modification of the repetition and orientation of excitation pulses, an image can be made Ti, T2, or proton density dominated. A proton density image shows static blood and fat as white and bone as black, while a Ti weighted image shows fat as white, blood as gray, and cerebrospinal fluid as black. T, weighted images tend to highlight pathology since pathologic tissue tends to have longer T, than normal In general, magnetic resonance imaging has greater intrinsic ability to distinguish between soft tissues than computerized tomography. It also has some ability to visualize moving blood. As the preceding discussion indicates, magnetic resonance is a richer and more complex modality than CT. Typically MRI has been more expensive than CT. Both MRI and Ct have been used primarily for anatomic imaging, but mRI has the potential h more important modality in the next decade Defining Terms Computerized axial tomography(CATscan, CT): A form of medical imaging based upon the linear attenu ation coefficient of x-rays in which a tomographic image is reconstructed from computer-based analy of a multiplicity of x-ray projections taken at different angles around the body. Magnetic resonance imaging(MRI, NMR): Aform of medical imaging with tomographic display which represents the density and bonding of protons(primarily in water)in the tissues of the body, based upon the ability of certain atomic nuclei in a magnetic field to absorb and reemit electromagnetic radiation at specific frequencies. Positron emission tomography(PET scan): A form of tomographic medical imaging based upon the density of positron-emitting radionuclides in an object. Single photon emission computed tomography(SPECT): A form of tomographic medical imaging based upon the density of gamma ray-emitting radionuclides in the body. Tomography: A method of image presentation in which the data is displayed in the form of individual slices that represent planar sections of the object. Related Topic 35.1 Maxwell References L. Axel, P.H. Arger, and R. Zimmerman, Applications of computerized tomography to diagnostic radiology, Proceedings of the IEEE, vol 71, no 3, P. 293, March 1983 K.R. Castleman, Digital Image Processing, Englewood Cliffs, N J. Prentice-Hall, 1979 E. Coleman, Single photon emission computed tomography and positron emission tomography, Cancer, l.67(4 Suppl.,pp.1261-1270,Feb.1991 c2000 by CRC Press LLC
© 2000 by CRC Press LLC we see that the detected signal S(tx,ty) is the two-dimensional Fourier transform of the magnetic resonance signal s(x,y) with u = gGxtx/2p, v = gGyty/2p. The magnetic resonance signal s(x,y) depends on the precise sequence of pulses of magnetic energy used to perturb the nuclei. For a typical sequence known as spin-echo consisting of a 90-degree pulse followed by a 180-degree pulse spaced at time t with the data collection at te = 2t, and tr being the repetition time between 90-degree pulses, the detected magnetic resonance signal can be expressed s(x,y) = r(1 – e–tr/T1)(e–te/T2) where r is the proton density, and T1 (the spin-lattice decay time) and T2 (the spin-spin decay time) are constants of the material related to the bonding of water in cells [Wolf and Popp, 1984]. Typically T1 ranges from 0.2 to 1.2 seconds, while T2 ranges from 0.05 to 0.15 seconds. By modification of the repetition and orientation of excitation pulses, an image can be made T1, T2, or proton density dominated. A proton density image shows static blood and fat as white and bone as black, while a T1 weighted image shows fat as white, blood as gray, and cerebrospinal fluid as black. T2 weighted images tend to highlight pathology since pathologic tissue tends to have longer T2 than normal. In general, magnetic resonance imaging has greater intrinsic ability to distinguish between soft tissues than computerized tomography. It also has some ability to visualize moving blood. As the preceding discussion indicates, magnetic resonance is a richer and more complex modality than CT. Typically MRI has been more expensive than CT. Both MRI and CT have been used primarily for anatomic imaging, but MRI has the potential through spectroscopy (visualization of other nuclei than hydrogen) to become a factor in physiologic imaging. Thus, it can be anticipated that magnetic resonance imaging will continue to increase and become an even more important modality in the next decade. Defining Terms Computerized axial tomography (CATscan, CT): A form of medical imaging based upon the linear attenuation coefficient of x-rays in which a tomographic image is reconstructed from computer-based analysis of a multiplicity of x-ray projections taken at different angles around the body. Magnetic resonance imaging (MRI, NMR): Aform of medical imaging with tomographic display which represents the density and bonding of protons (primarily in water) in the tissues of the body, based upon the ability of certain atomic nuclei in a magnetic field to absorb and reemit electromagnetic radiation at specific frequencies. Positron emission tomography (PET scan): A form of tomographic medical imaging based upon the density of positron-emitting radionuclides in an object. Single photon emission computed tomography (SPECT): A form of tomographic medical imaging based upon the density of gamma ray-emitting radionuclides in the body. Tomography: A method of image presentation in which the data is displayed in the form of individual slices that represent planar sections of the object. Related Topic 35.1 Maxwell Equations References L. Axel, P.H. Arger, and R. Zimmerman, “Applications of computerized tomography to diagnostic radiology,” Proceedings of the IEEE, vol. 71, no. 3, p. 293, March 1983. K.R. Castleman, Digital Image Processing, Englewood Cliffs, N.J.: Prentice-Hall, 1979. R.E. Coleman, “Single photon emission computed tomography and positron emission tomography,” Cancer, vol. 67 (4 Suppl.), pp. 1261–1270, Feb. 1991
P.M. Hurculak, Positron emission tomography, Canadian Journal of Medical Radiation Technology, vol. 18, G E. Knoll,Single-Photon emission computed tomography, Proceedings of the IEEE, vol. 71, no 3, P. 320, A Macovski, Medical Imaging Systems, Englewood Cliffs, N]: Prentice-Hall, 1983. H.R. Schelbert, Future perspectives: Diagnostic possibilities with positron emission tomography, " Roentgen Blaetter, vol. 43, no 9, PP. 384-390, Sept. 1990 G L. Wolf and C. Popp, NMR, A Primer for Medical Imaging, Thorofare, N J. Slack, Inc., 1984 Further information The journal IEEE Transactions on Medical Imaging describes advances in imaging techniques and image pro- cessing. Investigative Radiology published by the Association of University Radiologists, emphasizes research carried out by hospital-based physicists and engineers. Radiology, published by the North American Society of Radiologists, contains articles which emphasize clinical applications of imaging technology. Diagnostic imaging publishing by Miller Freeman, Inc, is a good source of review articles and information on the imaging 116.2 Ultrasound Leon a. frizzell Ultrasound, acoustic waves at frequencies higher than those audible by humans, has developed over th 35 years into an indispensable clinical diagnostic tool. Currently, ultrasound is used to image most parts body. More than half of all pregnant women in the United States are examined with ultrasound. This widespread utilization has resulted from ultrasounds proven clinical utility for imaging soft tissues compared to more expensive imaging techniques. The development of ultrasound, particularly for fetal examinations, has also been fostered by its safety record; no case of an adverse biological effect induced by diagnostic ultrasound has ver been reported in humans [AIUM, 1988]. Diagnostic ultrasound systems are used primarily for soft tissue imaging, motion detection, and flow mea- surement. Except for some Doppler instruments, these systems operate in a pulse-echo mode. a brief summary of some of the fundamentals of acoustic wave propagation and the principles of ultrasound imaging follows. als of a Unlike electromagnetic waves, acoustic waves require a medium for propagation. The acoustic wave phenom enon causes displacement of particles(consisting of many molecules), which results in pressure and density hanges within the medium. For a traveling sinusoidal wave, the variation in acoustic pressure( the difference between the total and ambient pressure), excess density, particle displacement, particle velocity, and particle acceleration can all be represented by the form p=Pe-aux cos(ot-kx) (116.1) for a wave propagating in the positive x direction, where p is the pressure(or one of the other parameters listed above), P is its amplitude, o is the angular frequency, and @= 2nf where f is the frequency in hertz, k is the propagation constant and k=o/c where c is the propagation speed, a is the attenuation coefficient, and t is the time. The wave can experience significant attenuation, as represented by the exponential decay of amplitude with distance, during propagation in tissues. The attenuation coefficient varies greatly among tissues [ Goss et al., 1978, 1980; Haney and OBrien, 1986] but is low for most body fluids, much higher for solid tissues, and very high for bone and lung(see Table 116.1). The skin depth is the distance that the wave can propagate before being attenuated to e of its original amplitude and is thus simply the inverse of the attenuation coefficient. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC P.M. Hurculak, “Positron emission tomography,” Canadian Journal of Medical Radiation Technology, vol. 18, no. 1, March 1987. G.F. Knoll, “Single-photon emission computed tomography,” Proceedings of the IEEE, vol. 71, no. 3, p. 320, March 1983. A. Macovski, Medical Imaging Systems, Englewood Cliffs, N.J.: Prentice-Hall, 1983. H.R. Schelbert, “Future perspectives: Diagnostic possibilities with positron emission tomography,” Roentgen Blaetter, vol. 43, no. 9, pp. 384–390, Sept. 1990. G.L. Wolf and C. Popp, NMR, A Primer for Medical Imaging, Thorofare, N.J.: Slack, Inc., 1984. Further Information The journal IEEE Transactions on Medical Imaging describes advances in imaging techniques and image processing. Investigative Radiology, published by the Association of University Radiologists, emphasizes research carried out by hospital-based physicists and engineers. Radiology, published by the North American Society of Radiologists, contains articles which emphasize clinical applications of imaging technology. Diagnostic Imaging, publishing by Miller Freeman, Inc., is a good source of review articles and information on the imaging marketplace. 116.2 Ultrasound Leon A. Frizzell Ultrasound, acoustic waves at frequencies higher than those audible by humans, has developed over the past 35 years into an indispensable clinical diagnostic tool. Currently, ultrasound is used to image most parts of the body. More than half of all pregnant women in the United States are examined with ultrasound. This widespread utilization has resulted from ultrasound’s proven clinical utility for imaging soft tissues compared to more expensive imaging techniques. The development of ultrasound, particularly for fetal examinations, has also been fostered by its safety record; no case of an adverse biological effect induced by diagnostic ultrasound has ever been reported in humans [AIUM, 1988]. Diagnostic ultrasound systems are used primarily for soft tissue imaging, motion detection, and flow measurement. Except for some Doppler instruments, these systems operate in a pulse-echo mode. A brief summary of some of the fundamentals of acoustic wave propagation and the principles of ultrasound imaging follows. Fundamentals of Acoustics Unlike electromagnetic waves, acoustic waves require a medium for propagation. The acoustic wave phenomenon causes displacement of particles (consisting of many molecules), which results in pressure and density changes within the medium. For a traveling sinusoidal wave, the variation in acoustic pressure (the difference between the total and ambient pressure), excess density, particle displacement, particle velocity, and particle acceleration can all be represented by the form p = P e –ax cos(wt – kx) (116.1) for a wave propagating in the positive x direction, where p is the pressure (or one of the other parameters listed above), P is its amplitude, w is the angular frequency, and w = 2pf where f is the frequency in hertz, k is the propagation constant and k = w/c where c is the propagation speed, a is the attenuation coefficient, and t is the time. The wave can experience significant attenuation, as represented by the exponential decay of amplitude with distance, during propagation in tissues. The attenuation coefficient varies greatly among tissues [Goss et al., 1978, 1980; Haney and O’Brien, 1986] but is low for most body fluids, much higher for solid tissues, and very high for bone and lung (see Table 116.1). The skin depth is the distance that the wave can propagate before being attenuated to e–1 of its original amplitude and is thus simply the inverse of the attenuation coefficient
TABLE 116.1 Approximate Ultrasonic Attenuation Coefficient, Speed, and Characteristic ic Impedance for Water and Selected Tissues at 3.5 MHz Attenuation Coefficient Speed Characteristic Impedance (m-) (10°Pas/m Water Amniotic fluid Muscle 172 5.70 Lun Ultrasound is typically used to image soft body tissues such as liver, but the sound beam often travels through fluids, for example, through amniotic fluid when imaging the fetus. Generally, bone and lung are not imaged with ultrasound. The attenuation processes include absorption, which is the conversion of acoustic energy to heat, and scattering, which will be addressed later. The attenuation increases roughly linearly with frequency in the 2-to 10-MHz range typically used for medical imaging. This range represents a compromise between increased penetration at lower frequencies(because of decreased attenuation) and improved resolution asso ciated with higher frequencies as discussed below. Thus, the lower frequencies are used when greater penetration is required, such as for fetal imaging in the obese patient, and higher frequencies for lesser penetration, such as the examination of peripheral vascular flow. When an acoustic wave impinges on an interface between two media of different specific acoustic impedance, a portion of the incident energy is reflected. For normal incidence on an infinite plane interface, the pressure reflection coefficient is given by [Kinsler et al., 1982 R=22-2 (116.2) 22+z1 where z, and z, are the specific acoustic impedance of the incident and transmitting media, respectively. For a plane wave the specific acoustic impedance is equal to the characteristic impedance which is the product of the density and acoustic speed in the medium(see Table 116.1). The speed is dependent upon the density and the elastic properties of the medium. Thus, at an interface between media exhibiting different densities or elastic properties, i.e., compressibility, some acoustic energy will be reflected. Although the reflection coefficient at an interface between muscle and bone is large(approximately 0.54)the reflection coefficient between two soft tissues such as liver and muscle is quite small (approximately 0.006). Reflection at oblique incidence obeys Snell's law in the same way it applies to electromagnetic waves In addition to the specular reflection that occurs at an interface between two media of different specific acoustic impedance as described above (where any curvature along the interface is negligible over distances comparable to a wavelength), energy may also be scattered in all directions by inhomogeneities in the medium. An acoustic image is formed by using this scattered energy as well as specular reflections. The fraction of the incident energy reflected or scattered is very small for soft tissues. Although it is convenient to consider plane waves of infinite lateral extent, as was done above, real source generate finite beams of ultrasound. These sources may be unfocused, but for the typical diagnostic system they are focused. Figure 116.4 shows the acoustic field from a typical focused source. The source consists of piezoelectric transducer which converts electrical to acoustic energy and vice versa. Most transducers for medical applications are made from ceramic materials such as a lead zirconate titanate(PZT) mixture. For a circular perture these may be circular disks with a plano-concave lens mounted in front to produce spherical focusing Alternatively, the transducer itself may be a spherical segment that produces a focused field without a lens Some probes utilize electronic focusing methods. Such a phased array probe consists of many individual elements which can be excited with signals having a controlled delay with respect to one another such that the c2000 by CRC Press LLC
© 2000 by CRC Press LLC Ultrasound is typically used to image soft body tissues such as liver, but the sound beam often travels through fluids, for example, through amniotic fluid when imaging the fetus. Generally, bone and lung are not imaged with ultrasound. The attenuation processes include absorption, which is the conversion of acoustic energy to heat, and scattering, which will be addressed later. The attenuation increases roughly linearly with frequency in the 2- to 10-MHz range typically used for medical imaging. This range represents a compromise between increased penetration at lower frequencies (because of decreased attenuation) and improved resolution associated with higher frequencies as discussed below. Thus, the lower frequencies are used when greater penetration is required, such as for fetal imaging in the obese patient, and higher frequencies for lesser penetration, such as the examination of peripheral vascular flow. When an acoustic wave impinges on an interface between two media of different specific acoustic impedance, a portion of the incident energy is reflected. For normal incidence on an infinite plane interface, the pressure reflection coefficient is given by [Kinsler et al., 1982] (116.2) where z1 and z2 are the specific acoustic impedance of the incident and transmitting media, respectively. For a plane wave the specific acoustic impedance is equal to the characteristic impedance which is the product of the density and acoustic speed in the medium (see Table 116.1). The speed is dependent upon the density and the elastic properties of the medium. Thus, at an interface between media exhibiting different densities or elastic properties, i.e., compressibility, some acoustic energy will be reflected. Although the reflection coefficient at an interface between muscle and bone is large (approximately 0.54) the reflection coefficient between two soft tissues such as liver and muscle is quite small (approximately 0.006). Reflection at oblique incidence obeys Snell’s law in the same way it applies to electromagnetic waves. In addition to the specular reflection that occurs at an interface between two media of different specific acoustic impedance as described above (where any curvature along the interface is negligible over distances comparable to a wavelength), energy may also be scattered in all directions by inhomogeneities in the medium. An acoustic image is formed by using this scattered energy as well as specular reflections. The fraction of the incident energy reflected or scattered is very small for soft tissues. Although it is convenient to consider plane waves of infinite lateral extent, as was done above, real sources generate finite beams of ultrasound. These sources may be unfocused, but for the typical diagnostic system they are focused. Figure 116.4 shows the acoustic field from a typical focused source. The source consists of a piezoelectric transducer which converts electrical to acoustic energy and vice versa. Most transducers for medical applications are made from ceramic materials such as a lead zirconate titanate (PZT) mixture. For a circular aperture these may be circular disks with a plano-concave lens mounted in front to produce spherical focusing. Alternatively, the transducer itself may be a spherical segment that produces a focused field without a lens. Some probes utilize electronic focusing methods. Such a phased array probe consists of many individual elements which can be excited with signals having a controlled delay with respect to one another such that the TABLE 116.1 Approximate Ultrasonic Attenuation Coefficient, Speed, and Characteristic Impedance for Water and Selected Tissues at 3.5 MHz Attenuation Coefficient Speed Characteristic Impedance Tissue (m–1) (m/s) (106 Pa s/m) Water 0.2 1520 1.50 Amniotic fluid 0.7 1510 1.51 Blood 7 1550 1.60 Liver 35 1580 1.74 Muscle 50 1560 1.72 Bone 800 3360 5.70 Lung 1000 340 0.25 R z z z z = - + 2 1 2 1
